On a broilerproof rimmed baking sheet, toss the baguette pieces with 1 tablespoon of the oil. Broil until golden, 3 to 4 minutes.
In a large bowl, combine the beans, pickles, onion, vinegar, the remaining 3 tablespoons of oil, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Fold in the broiled baguette. Divide the mixture among bowls and top with the tuna.